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Metamath Proof Explorer

Theorem dfor2

Description: Logical 'or' expressed in terms of implication only. Theorem *5.25 of WhiteheadRussell p. 124. (Contributed by NM, 12-Aug-2004) (Proof shortened by Wolf Lammen, 20-Oct-2012)

		Ref	Expression
	Assertion	dfor2	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ( ( 𝜑 → 𝜓 ) → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.62	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ( 𝜑 → 𝜓 ) → 𝜓 ) )
2		pm2.68	⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜓 ) → ( 𝜑 ∨ 𝜓 ) )
3	1 2	impbii	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ( ( 𝜑 → 𝜓 ) → 𝜓 ) )